Different CSS for a custom page template

I have created a custom page template in my child theme of Thematic and named it page-template-listingsite.php. It shows as an option for a template when I make a new page.
I have seen how a alternate stylesheet can be used for a specific page, whether it is by ID number, or page name, but can the stylesheet be used whenever the page-template-listingsite.php is used?

So if you are needing minimal style changes, you could actually target the class of .page-template-template-page-fullpage-php (which is my full page template) and override the styles of other pages, this will be by far easier than adding another style sheet. Just depends on what you are trying to accomplish and how different the page is.